Simultaneous Multiscale Polyaffine Registration by Incorporating Deformation Statistics

Locally affine (polyaffine) image registration methods capture intersubject non-linear deformations with a low number of parameters, while providing an intuitive interpretation for clinicians. Considering the mandible bone, anatomical shape differences can be found at different scales, e.g. left or right side, teeth, etc. Classically, sequential coarse to fine registration are used to handle multiscale deformations, instead we propose a simultaneous optimization of all scales. To avoid local minima we incorporate a prior on the polyaffine transformations. This kind of groupwise registration approach is natural in a polyaffine context, if we assume one configuration of regions that describes an entire group of images, with varying transformations for each region. In this paper, we reformulate polyaffine deformations in a generative statistical model, which enables us to incorporate deformation statistics as a prior in a Bayesian setting. We find optimal transformations by optimizing the maximum a posteriori probability. We assume that the polyaffine transformations follow a normal distribution with mean and concentration matrix. Parameters of the prior are estimated from an initial coarse to fine registration. Knowing the region structure, we develop a blockwise pseudoinverse to obtain the concentration matrix. To our knowledge, we are the first to introduce simultaneous multiscale optimization through groupwise polyaffine registration. We show results on 42 mandible CT images.

Accurate and robust reconstruction of proximal femur from sparse intraoperative data and dense point distribution model for surgical navigation

Constructing a 3D surface model from sparse-point data is a nontrivial task. Here, we report an accurate and robust approach for reconstructing a surface model of the proximal femur from sparse-point data and a dense-point distribution model (DPDM). The problem is formulated as a three-stage optimal estimation process. The first stage, affine registration, is to iteratively estimate a scale and a rigid transformation between the mean surface model of the DPDM and the sparse input points. The estimation results of the first stage are used to establish point correspondences for the second stage, statistical instantiation, which stably instantiates a surface model from the DPDM using a statistical approach. This surface model is then fed to the third stage, kernel-based deformation, which further refines the surface model. Handling outliers is achieved by consistently employing the least trimmed squares (LTS) approach with a roughly estimated outlier rate in all three stages. If an optimal value of the outlier rate is preferred, we propose a hypothesis testing procedure to automatically estimate it. We present here our validations using four experiments, which include 1 leave-one-out experiment, 2 experiment on evaluating the present approach for handling pathology, 3 experiment on evaluating the present approach for handling outliers, and 4 experiment on reconstructing surface models of seven dry cadaver femurs using clinically relevant data without noise and with noise added. Our validation results demonstrate the robust performance of the present approach in handling outliers, pathology, and noise. An average 95-percentile error of 1.7-2.3 mm was found when the present approach was used to reconstruct surface models of the cadaver femurs from sparse-point data with noise added.

[Hyperreactive luteomas during pregnancy--symptoms and complications: a case report]

A 27-year-old Caucasian (gravida 2 para 1) presented in week 16 of her twin pregnancy with worsening of hyperandrogenic symptoms. In week 17, she developed an acute abdomen due to a twisted, incarcerated right ovary, which was surgically removed. Histological analysis revealed a diffuse steroid cell hyperplasia. Postsurgery testosterone levels fell temporarily within normal limits, diminishing the hyperandrogenic symptoms. Over time androgen levels rose again slowly above normal values with clinical worsening of hirsutism. In the 32nd week of gestation, a cesarean section of two healthy female infants was necessary due to the development of preeclampsia. An ovarian biopsy revealed again the picture of hyperreactio luteinalis. Postpartum peripheral hormone levels fell within normal limits and the hyperandrogenic symptoms subsided.

Flexible varieties and automorphism groups

Given an irreducible affine algebraic variety X of dimension n≥2 , we let SAut(X) denote the special automorphism group of X , that is, the subgroup of the full automorphism group Aut(X) generated by all one-parameter unipotent subgroups. We show that if SAut(X) is transitive on the smooth locus X reg , then it is infinitely transitive on X reg . In turn, the transitivity is equivalent to the flexibility of X . The latter means that for every smooth point x∈X reg the tangent space T x X is spanned by the velocity vectors at x of one-parameter unipotent subgroups of Aut(X) . We also provide various modifications and applications.

Frequency of Sobolev and quasiconformal dimension distortion

We study Hausdorff and Minkowski dimension distortion for images of generic affine subspaces of Euclidean space under Sobolev and quasiconformal maps. For a supercritical Sobolev map f defined on a domain in RnRn, we estimate from above the Hausdorff dimension of the set of affine subspaces parallel to a fixed m-dimensional linear subspace, whose image under f has positive HαHα measure for some fixed α>mα>m. As a consequence, we obtain new dimension distortion and absolute continuity statements valid for almost every affine subspace. Our results hold for mappings taking values in arbitrary metric spaces, yet are new even for quasiconformal maps of the plane. We illustrate our results with numerous examples.

On the signature of positive braids and adjacency for torus knots

The objects of study in this thesis are knots. More precisely, positive braid knots, which include algebraic knots and torus knots. In the first part of this thesis, we compare two classical knot invariants - the genus g and the signature σ - for positive braid knots. Our main result on positive braid knots establishes a linear lower bound for the signature in terms of the genus. In the second part of the thesis, a positive braid approach is applied to the study of the local behavior of polynomial functions from the complex affine plane to the complex numbers. After endowing polynomial function germs with a suitable topology, the adjacency problem arises: for a fixed germ f, what classes of germs g can be found arbitrarily close to f? We introduce two purely topological notions of adjacency for knots and discuss connections to algebraic notions of adjacency and the adjacency problem.

A second look at gauged supergravities from fluxes in M-theory

We investigate reductions of M-theory beyond twisted tori by allowing the presence of KK6 monopoles (KKO6-planes) compatible with N = 4 supersymmetry in four dimensions. The presence of KKO6-planes proves crucial to achieve full moduli stabilisation as they generate new universal moduli powers in the scalar potential. The resulting gauged supergravities turn out to be compatible with a weak G2 holonomy at N = 1 as well as at some non-supersymmetric AdS4 vacua. The M-theory flux vacua we present here cannot be obtained from ordinary type IIA orientifold reductions including background fluxes, D6-branes (O6-planes) and/or KK5 (KKO5) sources. However, from a four-dimensional point of view, they still admit a description in terms of so-called non-geometric fluxes. In this sense we provide the M-theory interpretation for such non-geometric type IIA flux vacua.

Bipartite graphs and quasipositive surfaces

We present a simple combinatorial model for quasipositive surfaces and positive braids, based on embedded bipartite graphs. As a first application, we extend the well-known duality on standard diagrams of torus links to twisted torus links. We then introduce a combinatorial notion of adjacency for bipartite graph links and discuss its potential relation with the adjacency problem for plane curve singularities.

N-terminal modifications improve the receptor affinity and pharmacokinetics of radiolabeled peptidic gastrin-releasing peptide receptor antagonists: examples of 68Ga- and 64Cu-labeled peptides for PET imaging

UNLABELLED Gastrin-releasing peptide receptors (GRPrs) are overexpressed on a variety of human cancers, providing the opportunity for peptide receptor targeting via radiolabeled bombesin-based peptides. As part of our ongoing investigations into the development of improved GRPr antagonists, this study aimed at verifying whether and how N-terminal modulations improve the affinity and pharmacokinetics of radiolabeled GRPr antagonists. METHODS The potent GRPr antagonist MJ9, Pip-d-Phe-Gln-Trp-Ala-Val-Gly-His-Sta-Leu-NH(2) (Pip, 4-amino-1-carboxymethyl-piperidine), was conjugated to 1,4,7-triazacyclononane, 1-glutaric acid-4,7 acetic acid (NODAGA), and 1,4,7-triazacyclononane-1,4,7-triacetic acid (NOTA) and radiolabeled with (68)Ga and (64)Cu. The GRPr affinity of the corresponding metalloconjugates was determined using (125)I-Tyr(4)-BN as a radioligand. The labeling efficiency of (68)Ga(3+) was compared between NODAGA-MJ9 and NOTA-MJ9 in acetate buffer, at room temperature and at 95°C. The (68)Ga and (64)Cu conjugates were further evaluated in vivo in PC3 tumor xenografts by biodistribution and PET imaging studies. RESULTS The half maximum inhibitory concentrations of all the metalloconjugates are in the high picomolar-low nanomolar range, and these are the most affine-radiolabeled GRPr antagonists we have studied so far in our laboratory. NODAGA-MJ9 incorporates (68)Ga(3+) nearly quantitatively (>98%) at room temperature within 10 min and at much lower peptide concentrations (1.4 × 10(-6) M) than NOTA-MJ9, for which the labeling yield was approximately 45% under the same conditions and increased to 75% at 95°C for 5 min. Biodistribution studies showed high and specific tumor uptake, with a maximum of 23.3 ± 2.0 percentage injected activity per gram of tissue (%IA/g) for (68)Ga-NOTA-MJ9 and 16.7 ± 2.0 %IA/g for (68)Ga-NODAGA-MJ9 at 1 h after injection. The acquisition of PET images with the (64)Cu-MJ9 conjugates at later time points clearly showed the efficient clearance of the accumulated activity from the background already at 4 h after injection, whereas tumor uptake still remained high. The high pancreas uptake for all radiotracers at 1 h after injection was rapidly washed out, resulting in an increased tumor-to-pancreas ratio at later time points. CONCLUSION We have developed 2 GRPr antagonistic radioligands, which are improved in terms of binding affinity and overall biodistribution profile. Their promising in vivo pharmacokinetic performance may contribute to the improvement of the diagnostic imaging of tumors overexpressing GRPr.

Distamycin-NA: A DNA Analog with an Aromatic Heterocyclic Polyamide Backbone. Part 1. Synthesis and structural analysis of monomers and dimers containing the nucleobase uracil

The synthesis of the monomeric building block 13 and its constitutional isomer 12 of a new type of DNA analog, distamycin-NA, is presented (Schemes 1 and 2). This building block consists of a uracil base attached to a thiophene core unit via a biaryl-like axis. Next to the biaryl-like axis on the thiophene chromophore, a carboxy and an amino substituent are located allowing for oligomerization via peptide coupling. The proof of constitution and the conformational preferences about the biaryl-like axis were established by means of X-ray analyses of the corresponding nitro derivatives 10 and 11. Thus, the uracil bases are propeller-twisted relative to the thiophene core, and bidentate H-bonds occur between two uracil bases in the crystals. The two amino-acid building blocks 12 and 13 were coupled to give the dimers 15 and 16 using dicyclohexylcarbodiimide (DCC) in THF/LiCl and DMF, respectively. While the dimer 15 showed no atropisomerism on the NMR time scale at room temperature, its isomer 16 occurred as distinct diastereoisomers due to the hindered rotation around its biaryl-like axis. Variable-temperature 1H-NMR experiments allowed to determine a rotational barrier of 19 ± 1 kcal/mol in 16. The experimental data were complemented by AM1 calculations.

4D/3D reduction of dualities: mirrors on the circle

We engineer a brane picture for the reduction of Seiberg dualities from 4D to 3D, valid also in the presence of orientifold planes. We obtain effective 3D dualities on the circle by T-duality, geometrizing the non-perturbative superpotential which is an affine Toda potential. When reducing to pure 3D, we define a double-scaling limit which creates a sector of interacting singlets, giving a unified mechanism for the brane reduction of dualities.

Probing the moduli dependence of refined topological amplitudes

With the aim of providing a worldsheet description of the refined topological string, we continue the study of a particular class of higher derivative couplings Fg,n in the type II string effective action compactified on a Calabi–Yau threefold. We analyse first order differential equations in the anti-holomorphic moduli of the theory, which relate the Fg,n to other component couplings. From the point of view of the topological theory, these equations describe the contribution of non-physical states to twisted correlation functions and encode an obstruction for interpreting the Fg,n as the free energy of the refined topological string theory. We investigate possibilities of lifting this obstruction by formulating conditions on the moduli dependence under which the differential equations simplify and take the form of generalised holomorphic anomaly equations. We further test this approach against explicit calculations in the dual heterotic theory.

Transmission electron microscopy of the bacterial nucleoid.

Water-containing biological material cannot withstand the vacuum of the transmission electron microscope. The classical solution to this problem has been to dehydrate chemically fixed biological samples and then embed them in resin. During such treatment, the bacterial nucleoid is especially prone to aggregation, which affects its global shape and fine structure. Initial attempts to deal with aggregation by optimizing chemical fixation yielded contradictory results. Two decades ago, the situation improved with the introduction of freeze-substitution. This method is based on dehydration of unfixed cryo-immobilized samples at low temperature, which substantially reduces aggregation. As a result, the global shape of the nucleoid can be fairly well defined. Overall, in actively growing bacteria, the nucleoids are dispersed and "coralline" but become more confined when growth ceases. However, it is usually impossible to determine the molecular arrangement of DNA in the nucleoids of freeze-substituted bacteria because crystallization and the subsequent removal of water during substitution result in unavoidable distortions at the ultrastructural level. Recently, cryo-electron microscopy of vitreous sections has enabled the fully hydrated bacterial nucleoid to be studied close to the native state. Such studies have revealed aspects of bacterial nucleoid organization that are not preserved by freeze-substitution, including locally parallel or twisted bundles of DNA filaments, which are more frequently observed once bacterial growth has stopped, whereas in actively growing bacteria, the DNA is seen to be in a mostly disordered pattern.

Nucleon and pion structure with lattice QCD simulations at physical value of the pion mass

We present results on the nucleon scalar, axial, and tensor charges as well as on the momentum fraction, and the helicity and transversity moments. The pion momentum fraction is also presented. The computation of these key observables is carried out using lattice QCD simulations at a physical value of the pion mass. The evaluation is based on gauge configurations generated with two degenerate sea quarks of twisted mass fermions with a clover term. We investigate excited states contributions with the nucleon quantum numbers by analyzing three sink-source time separations. We find that, for the scalar charge, excited states contribute significantly and to a less degree to the nucleon momentum fraction and helicity moment. Our result for the nucleon axial charge agrees with the experimental value. Furthermore, we predict a value of 1.027(62) in the MS¯¯¯¯¯ scheme at 2 GeV for the isovector nucleon tensor charge directly at the physical point. The pion momentum fraction is found to be ⟨x⟩π±u−d=0.214(15)(+12−9) in the MS¯¯¯¯¯ at 2 GeV.